SOLUTION: In a two-digit number, 5 times the units digit added to the tens digit equals 43. Five times the tens digit added to the units digit equals 47. Find the number

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Question 1146954: In a two-digit number, 5 times the units digit added to the tens digit equals 43. Five times the tens digit added to the units digit equals 47. Find the number
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let x = the value of the tens digit.
let y = the value of the ones digit.
the number is 10x + y.
example: in the number 57, 5 is the value of the tens digit and 7 is the value of the ones digit and the number is 10 * 5 + 7 = 57.
this is because each tens digit is worth 10 units while each units digit is worth 1 unit.
your equations are:
x + 5y = 43
5x + y = 47
multiply both sides of the first equation by 5 and leave the second equation as is to get:
5x + 25y = 215
5x + y = 47
subtract the second equation from the first to get:
24y = 168
solve for y to get:
y = 7
replace y with 7 in the second equation of 5x + y = 47 to get:
5x + 7 = 47
subtract 7 from both sides to get:
5x = 40
solve for x to get:
x = 8
replace x with 8 and y with 7 in both original equqations to get:
x + 5y = 43 becomes 8 + 35 = 43 which becomes 43 = 43 which is true.
5x + y = 47 becomes 40 + 7 = 47 which becomes 47 = 47 which is true.
both original equation are true when x = 8 and y = 7.
your number is 10x + y which is equal to 87.
that's your solution.
Answer by ikleyn(52921)   (Show Source): You can put this solution on YOUR website!
.
Let x be the ones digit and y be the tens digit.


    5x +   y = 43      (1)
     x  + 5y = 47      (2)


Add the equations.  You will get


    6x + 6y = 43 + 47 = 90

     x + y            = 90/6 = 15.   (3)


Express  x = 15 - y and substitute it into equation (1). You will get


    5*(15-y) + y = 43

    75 - 5y + y = 43

    -4y         = 43 - 75 = -32

     y                    =  = 8.


Then from (3)  x = 15-y = 15-8 = 7.


ANSWER.  The number is 87.

Solved.


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